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Jornelecrearlqx2un

Jornelecrearlqx2un

Answered question

2022-06-01

Prove resemblance between n = 1 sin ( 2 n x ) and cot x

Answer & Explanation

Selena Pratt

Selena Pratt

Beginner2022-06-02Added 5 answers

From the formula
k = 1 n sin ( 2 k θ ) = 1 2 cot θ 1 2 cos ( 2 n + 1 ) θ sin θ ,
it seems that the upper envelope is given by 1 2 ( cot θ + | csc θ | ) and likewise the lower envelope is given by 1 2 ( cot θ | csc θ | ). When 0 < θ < π, we can simplify them as
1 2 ( cot θ + csc θ ) = 1 2 cot θ 2 and 1 2 ( cot θ csc θ ) = 1 2 tan θ 2 .

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